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Help! Test tomorrow! How should I solve this?

Help! Test tomorrow! How should I solve this?-example-1
User Youn Elan
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1 Answer

3 votes

Answer:

B. 33

Explanation:

Step 1: Find total measure of ∠R:

  • Since we're told that ∠R and ∠Q are bisected by RB and QA, the two angles are divided into two congruent angles.
  • Therefore, the 38° is 1/2 the total measure of ∠R
  • Thus, entire measure of R is 76 as 38 + 38 = 76.

Step 2: Find total measure, m, of ∠Q:

  • The sum of the measures of the interior angles of a triangle always equals 180.
  • Thus, we can find the measure of ∠Q by subtracting the sum of the measures of ∠R and ∠P from 180:

m∠P + m∠Q + m∠R = 180

m∠Q = 180 - (m∠P + m∠R)

m∠Q = 180 - (60 + 76)

m∠Q = 180 - 136

m∠Q = 44°

Since QA bisects ∠Q into two congruent angles, we divide 44 by 2 to find the measures of each angle made by the bisector: 44/2 = 22.

Step 3: Find x by setting the sum of the 38° angle, the 22° angle, and angle C equal to 180:

38 + (3x + 21) + 22 = 180

60 + 3x + 21 = 180

81 + 3x = 180

3x = 99

x = 33

Thus, x equals 33.

User Chanandrei
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